Handbook of Geometric Computing

This handbook brings together the most recent advances in the application of geometric computing to the most important fields related to the endeavor of building perception action systems: computer vision, robotics, image processing and understanding, pattern recognition, computer graphics, quantum computers, brain theory and neural networks. Coverage introduces diverse, powerful geometric methods in a unified manner, covering geometry theory and geometric computing methods related to the design of perception and action systems, intelligent autonomous systems and intelligent machines. It is aimed at a broad audience of applied mathematicians, physicists, computer scientists, and engineers. The book is ideal for specialists working in a particular field or for those who are interested in procedures for dealing with concurrent techniques of different fields such as the design of perception action systems.

Consulting textbook for graduate courses and for researchers seeking powerful geometric methods Great use for specialists working in a particular field or for those who are interested in procedures for dealing with concurrent techniques of different fields like in the design of perception action systems Emphasizes the modern ways and formalisms for the representation and processing of geometric entities and the numerical solutions of equations involving geometric constraints often derived from the problem context The knowledge of all application domains is not required, only very basic notions on geometry The mathematical background will be presented at the beginning of each chapter Includes supplementary material: sn.pub/extras

Autorentext

Researcher in geometric computing for cognitive systems

Full Professor at the Computer Science Department of the

Center of Research and Advanced Studies CINVESTAV, Guadalajara, Mexico

Author and editor of books on geometric computing for computer science and engineering, reviewer, chair and active organiser of workshops and conferences on geometric computing for fields related to the design and building of perception action systems. Areas of research interest: pattern recognition, computer vision, neurocomputing, robotics, multidimensional image analysis, applications of Lie algebras and Clifford geometric algebra to cognitive systems.

Inhalt
Neuroscience.- Spatiotemporal Dynamics of Visual Perception Across Neural Maps and Pathways.- Symmetry, Features, and Information.- Neural Networks.- Geometric Approach to Multilayer Perceptrons.- A Lattice Algebraic Approach to Neural Computation.- Eigenproblems in Pattern Recognition.- Image Processing.- Geometric Framework for Image Processing.- Geometric Filters, Diffusion Flows, and Kernels in Image Processing.- Chaos-Based Image Encryption.- Computer Vision.- One-Dimensional Retinae Vision.- Three-Dimensional Geometric Computer Vision.- Dynamic % MathType!MTEF!2!1!+- % feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D % aebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbbf9v8qqaq % Fr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qq % Q8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaatu % uDJXwAK1uy0HwmaeHbfv3ySLgzG0uy0Hgip5wzaGqbaiab-9q8qnaa % CaaaleqabaWexLMBb50ujbqehq0BYngALnhDLjhitnMCPbhDG0evaG % GbaKqzafGae4NBa4gaaaaa!4FF9! $$\mathcal{P}^n $$ to % MathType!MTEF!2!1!+- % feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D % aebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbbf9v8qqaq % Fr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qq % Q8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaatu % uDJXwAK1uy0HwmaeHbfv3ySLgzG0uy0Hgip5wzaGqbaiab-9q8qnaa % CaaaleqabaWexLMBb50ujbqehq0BYngALnhDLjhitnMCPbhDG0evaG % GbaKqzafGae4NBa4gaaaaa!4FF9! $$\mathcal{P}^n $$ Alignment.- Detecting Independent 3D Movement.- Perception and Action.- Robot Perception and Action Using Conformal Geometric Algebra.- Uncertainty in Geometric Computations.- Uncertainty Modeling and Geometric Inference.- Uncertainty and Projective Geometry.- The Tensor Voting Framework.- Computer Graphics and Visualization.- Methods for Nonrigid Image Registration.- The Design of Implicit Functions for Computer Graphics.- Geometry and Robotics.- Grassmann-Cayley Algebra and Robotics Applications.- Clifford Algebra and Robot Dynamics.- Geometric Methods for Multirobot Optimal Motion Planning.- Reaching and Motion Planning.- The Computation of Reachable Surfaces for a Specified Set of Spatial Displacements.- Planning Collision-Free Paths Using Probabilistic Roadmaps.